复映射f(z,c)=z^(-2)+c倍周期芽苞Julia集的标度性  

Multiplier Periodic Buds of Complex Mapping f(z,c)=z^(-2)+c

作　　者：宋春林[1] 邓学工[1] 李志勇[1] 朱伟勇[2] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004 [2]东北大学计算中心,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2003年第5期433-436,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(69974008);教育部博士学科点专项科研基金资助项目(2000014512)

摘　　要：利用逃逸时间算法绘制了复映射f(z,c)=z-2+c倍周期超吸引点处Julia集的分形图,指出M集与J集之间的紧密联系·通过大量试验,得到了构造任意倍周期超吸引点处符号序列的一个规律,由此规律提出一种构造字提升方程的算法,并利用该算法获得了主轴上超吸引点的精确解以及Julia集的不动点·研究发现Julia集存在两个普适常数,并通过试验在非主轴上验证了普适常数的正确性·?Julia set is a kind of Mandelbrot set which follows the rules of uncountable,limited and infinite nesting. Using escape time algorithm, the Julia sets' fractal image is protracted on the multiplier periodic superattracted points of complex mapping f(z,c)=z-2+c. It is found that there is a tight relation between the Mandelbrot set and Julia set. The rule of constructing symbol sequence on arbitrary multiplier periodic superattracted points is proposed based on lots of experiments. A novel algorithm of constructing wordlifting formula is presented. The accurate solution of superattracted points on principal axis and the immovable point of Julia set is obtained. It is also found that there are two general constants of Julia set. The constants are validated on the nonprincipal axis.

关 键 词：逃逸时间算法 JULIA集 分岔图 字提升方程 标度因子 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]